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authorsiveshs <siveshs@gmail.com>2010-07-03 04:06:44 +0000
committerbnewbold <bnewbold@adelie.robocracy.org>2010-07-03 04:06:44 +0000
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section 3 editing
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@@ -103,7 +103,12 @@ inner product, (f,g) & = & \int_0^{2\pi} f g \,dx\\
$$
This is the inner product of 2 real-number functions. For a function on complex numbers, the above definition must be altered as follows:
---> altered function here
+$$
+\begin{array}{ccl}
+inner product, (f,g) & = & \int_0^{2\pi} f \vec g \,dx\\
+\mid f \mid ^2 = (f, f) & = & \int_0^{2\pi} f^2 \,dx\\
+\end{array}
+$$
*Note: These are purely definitions, and we are now definining the inner product to ensure that inner product of f and f is a real number.*